Antioxidant treatment of human disease has met with mixed success. Factors that lead to oxidative stress in living systems are complicated, and as a result, the actions of antioxidants may seem paradoxical. There is a great deal of evidence for increased oxidative stress in uremia. The rationale for this proposal stems from emerging evidence for efficacy of vitamin E in uremia. The investigators believe that intimal hyperplasia in hemodialysis vascular access represents a unique model of oxidative damage to vascular tissue. Complications of hemodialysis access are a major cause of morbidity and the most frequent single reason for hospitalization among patients with end stage renal disease (ESRD). In vivo and in vitro, oxidative stress stimulates cell growth factors and regulatory mechanisms that lead to the characteristic lesion of access failure, intimal hyperplasia. The central hypothesis to be tested by this project is that oxidative stress is a major (and modifiable) pathogenetic trigger for vascular access complications in patients with ESRD. In elucidating the roles of oxidative stress in the pathophysiology of access failure, the goal is to discover diagnostic factors that can lead to accurate indications for antioxidant therapy. In testing antioxidant medication, the investigators hope to slow progression of intimal hyperplasia in hemodialysis access. Because antioxidant therapy is not currently routine in patients with uremia, the proposal is a pilot study. Data obtained in these specific aims will be used to design large-scale testing of the efficacy of vitamin E (alpha-tocopherol). Specific Aim A: To identify predictors of vascular access venous outflow stenosis or thrombosis, focusing on circulating and histologic markers indicative of the effects of oxidative stress. Specific Aim B: To determine the efficacy of chronic administration of an antioxidant (alpha-tocopherol) in the prevention of intimal hyperplasia and thrombosis of the hemodialysis access. Specific Aim C: To compare the success rates of prophylactic angioplasty when non-invasive techniques demonstrate decreased flow in the hemodialysis access in alpha-tocopherol-treated versus placebo-treated patients.